Method and apparatus for removing tissue autofluorescence

ABSTRACT

Techniques for removing image autoflourescence from fluorescently stained biological images are provided herein. The techniques utilize non-negative matrix factorization that may constrain mixing coefficients to be non-negative. The probability of convergence to local minima is reduced by using smoothness constraints. The non-negative matrix factorization algorithm provides the advantage of removing both dark current and autofluorescence.

BACKGROUND

The invention relates generally to methods and systems for removinginherent autofluorescence and the contribution of dark current fromimages of biological materials.

Recent advances in imaging and microscopy technologies combined with thedevelopment of fluorescent probes have allowed researchers to studyvariations in movement, distribution, and concentration of variousmolecular markers. In many such studies, fluorescent probes with abinding specificity to one or more cellular molecules are introducedinto a sample. Images are obtained of the sample, for example withfluorescence microscopy, and these images may be processed and furtheranalyzed to determine the amount of fluorescence in the image, which mayprovide information about the cellular marker. Accurate detection andanalysis of the contribution of fluorescence from the fluorescent probesmay be critical for many microscopy applications, such as molecularpathology imaging. For example, the fluorescence in the image may beanalyzed to determine if the samples contain markers associated withspecific clinical conditions, such as cancer.

Cells in many organisms have inherent fluorescence, which may bereferred to as autofluorescence. This autofluorescence can interferewith the analysis of images obtained of these cells. For example,autofluorescence may reduce signal detection sensitivity by masking thefluorescence of the probe of interest. In addition, autofluorescence mayalso decrease the specificity of detection by providing false positiveresults.

The extent of autofluorescence may be limited by treating the samplewith certain dyes or chemicals prior to image acquisition. For example,the dye pontiamine sky blue is used to stain samples and quenchautofluorescence. However, these treatment techniques involve furthermanipulation of the biological sample, which may degrade the quality ofthe sample itself. In addition, strategies for autofluorescence removalhave been proposed that involve the image acquisition hardware, such asusing lasers for excitation or polarized light. However, thesetechniques may not be suitable with standard fluorescent microscopes inwidespread use.

Digitally acquired fluorescence microscope images can also be processedretrospectively using software methods, to separate autofluorescencefrom the relevant dye fluorescence. Some of these methods rely onacquiring estimates of the pure autofluorescence signal and using themto remove autofluorescence from images containing both dye andautofluorescence signals by a weighted subtraction. Others usestatistical correlation techniques to correct for the additiveautofluorescence signal. While these techniques may be more costeffective, they may not be able to completely remove theautofluorescence component from fluorescence microscopy images. Forexample, spectral unmixing methods often require prior knowledge of theamount of autofluorescence in the sample.

In addition, cell or tissue images may also include a certain amount ofnoise contributed by the acquisition system itself. For example, “darkcurrent,” represents the response, in the absence of light, of manytypes of electromagnetic radiation receptors. Generally, dark current isdealt with by a simple subtraction. However, there is no imageprocessing method that deals with both autofluorescence and darkcurrent.

BRIEF DESCRIPTION

The methods and systems of the invention generally involve a fullyautomated technique for the removal of autofluorescence from variousimages, each containing an unknown combination of autofluorescence andfluorescence of interest. The acquired images may be subjected to anon-negative matrix factorization algorithm to remove autofluorescence.In addition, the methods and systems of the invention also remove darkcurrent noise from the fluorescent images.

The present techniques provide a method for reducing autofluorescence inan image of a biological material that includes: accessing image datafrom two or more images of the biological material, wherein at least oneof the images is fluorescently stained for a marker of interest andwherein at least one of the images is a reference image; analyzing theimage data of the two or more images using a non-negative matrixfactorization algorithm to generate an estimate of the autofluorescencein at least one of the two or more images; and generating an output of acorrected image with reduced autofluorescence.

The present techniques also provide a computer-readable medium thatincludes instructions for: accessing image data from two or more imagesof the biological material, wherein at least one of the images isfluorescently stained for a marker of interest and wherein at least oneof the images is a reference image; analyzing the image data of the twoor more images using a non-negative matrix factorization algorithm togenerate an estimate of the autofluorescence in at least one of the twoor more images; and generating an output of a corrected image withreduced autofluorescence.

The present techniques also provide an image analysis system thatincludes a processor adapted to receive image data from two or moreimages of the biological material, wherein at least one of the images isfluorescently stained for a marker of interest and wherein at least oneof the images is a reference image the processor adapted to runinstructions for: analyzing the image data of the two or more imagesusing a non-negative matrix factorization algorithm to generate anestimate of the autofluorescence in at least one of the two or moreimages; and generating an output of a corrected image with reducedautofluorescence.

DRAWINGS

These and other features, aspects, and advantages of the presentinvention will become better understood when the following detaileddescription is read with reference to the accompanying drawings in whichlike characters represent like parts throughout the drawings, wherein:

FIG. 1 is a diagrammatical view of an exemplary system for use inacquiring image data of cells in accordance with aspects of the presenttechnique;

FIG. 2A is a diagrammatical view of an exemplary two-step imageacquisition system in accordance with aspects of the present technique;

FIG. 2B is a diagrammatical view of an exemplary extra channel imageacquisition system in accordance with aspects of the present technique;

FIG. 3A is a ground truth image of fluorescent beads with noautofluorescence;

FIG. 3B is an image of the fluorescent beads with autofluorescence;

FIG. 3C is an image with the autofluorescence removed according to thepresent techniques;

FIG. 4 shows mean receiver operator characteristic curves (ROCs) for 35tissue samples;

FIG. 5A is an image of a human breast tissue sample sainted with cy5bound to estrogen receptor; and

FIG. 5B is the image of FIG. 5A with the autofluorescence removedaccording to the present techniques.

DETAILED DESCRIPTION

The methods and systems of the present techniques may provide theadvantage of improving image analysis for fluorescently stained images.Such techniques may preserve signal fluorescence while reducing oreliminating autofluorescence, as well as dark current. The techniquesincrease the resulting signal-to-autofluorescence ratio and the overallsensitivity of detection. These fully automatic systems and methodsoperate without user intervention and complicated and expensiveinstrumentation. The methods and systems are adaptable to a wide arrayof biological samples, including tissue micro arrays. However, they arenot limited to use with tissue micro arrays and may be applied to anyfluorescence imaging application.

The present techniques provide an automatic autofluorescence removalmethod for fluorescent spectroscopy, based on a realistic physicalmodel. In one embodiment, the image processing technique provided hereinuses a non-negative matrix factorization algorithm with reducedprobability for convergence to local minima. Smoothing the estimatedautofluorescence and autofluorescence-reduced images at every stage ofthe iteration with a Gaussian kernel helps to constrain the computedsolution by taking into account that changes in the image on a scalesmaller than the standard deviation of the kernel may be irrelevant tothe analysis. Unlike previous spectral mixing models used forautofluorescence removal, the method provided herein may utilize amixing matrix that is estimated from image data, rather than beingprovided by the user. In addition, because the matrices used in themethod have non-negative entries, a model may be generated that isphysically interpretable. Furthermore, the algorithm provided hereinautomatically compensates for unknown dark current terms, d_(i), thatmay be present in images acquired by fluorescent microscopy. This isachieved by the novel non-negative matrix factorization algorithm usedby the present techniques.

The present techniques provide systems and methods for image analysis.In certain embodiments, it is envisioned that the present techniques maybe used in conjunction with previously acquired images, for example,stored images, in retrospective studies. In other embodiments, thepresent techniques may be used in conjunction with an image acquisitionsystem. An exemplary imaging system 10 capable of operating inaccordance with the present technique is depicted in FIG. 1. Generally,the imaging system 10 includes an imager 12 that detects signals andconverts the signals to data that may be processed by downstreamprocessors. As described more fully below, the imager 12 may operate inaccordance with various physical principles for creating the image data.In certain embodiments, the imager 12 may include a fluorescentmicroscope or other suitable imager for analyzing fluorescently stainedimages. In general, however, the imager 12 creates image data indicativeof a biological sample, including a sample 14, shown here as beingmultiple samples on a tissue micro array. The image data may be eitherin a conventional medium, such as photographic film, or in a digitalmedium.

The imager 12 operates under the control of system control circuitry 16.The system control circuitry 16 may include a wide range of circuits,such as illumination source control circuits, timing circuits, circuitsfor coordinating data acquisition in conjunction with sample movements,circuits for controlling the position of light sources and detectors,and so forth. In the present context, the system control circuitry 16may also include computer-readable memory elements, such as magnetic oroptical storage media, for storing programs and routines executed by thesystem control circuitry 16 or by associated components of the system10. The stored programs or routines may include programs or routines forperforming all or part of the present technique.

Image data acquired by the imager 12 may be processed by the imager 12,for a variety of purposes, for example to convert the acquired data orsignal to digital values, and provided to data acquisition circuitry 18.The data acquisition circuitry 18 may perform a wide range of processingfunctions, such as adjustment of digital dynamic ranges, smoothing orsharpening of data, as well as compiling of data streams and files,where desired.

The data acquisition circuitry 18 may also transfer acquisition imagedata to data processing circuitry 20, where additional processing andanalysis may be performed. Thus, the data processing circuitry 20 mayperform substantial analyses of image data, including ordering,sharpening, smoothing, feature recognition, and so forth. In addition,the data processing circuitry 20 may receive data for one or more samplesources, (e.g. multiple spots on a tissue micro array). The processedimage data may be stored in short or long term storage devices, such aspicture archiving communication systems, which may be located within orremote from the imaging system 10 and/or reconstructed and displayed foran operator, such as at the operator workstation 22.

In addition to displaying the reconstructed image, the operatorworkstation 22 may control the above-described operations and functionsof the imaging system 10, typically via an interface with the systemcontrol circuitry 16. The operator workstation 22 may include one ormore processor-based components, such as general purpose or applicationspecific computers 24. In addition to the processor-based components,the computer 24 may include various memory and/or storage componentsincluding magnetic and optical mass storage devices and internal memory,such as RAM chips. The memory and/or storage components may be used forstoring programs and routines for performing the techniques describedherein that are executed by the computer 24 or by associated componentsof the system 10. Alternatively, the programs and routines may be storedon a computer accessible storage and/or memory remote from the operatorworkstation 22 but accessible by network and/or communication interfacespresent on the computer 24.

The computer 24 may also comprise various input/output (I/O) interfaces,as well as various network or communication interfaces. The various I/Ointerfaces may allow communication with user interface devices, such asa display 26, keyboard 28, mouse 30, and printer 32, that may be usedfor viewing and inputting configuration information and/or for operatingthe imaging system 10. The various network and communication interfacesmay allow connection to both local and wide area intranets and storagenetworks as well as the Internet. The various I/O and communicationinterfaces may utilize wires, lines, or suitable wireless interfaces, asappropriate or desired.

More than a single operator workstation 22 may be provided for animaging system 10. For example, an imaging scanner or station mayinclude an operator workstation 22 which permits regulation of theparameters involved in the image data acquisition procedure, whereas adifferent operator workstation 22 may be provided for manipulating,enhancing, and viewing results and reconstructed images.

These methods and systems may be used to image and analyze a biologicalsample to discern the presence, absence, concentration, and/or spatialdistribution of one or more biological materials or targets in abiological sample or tissue. As used herein, the term “biologicalmaterial” refers to material obtained from, or located in, a biologicalsubject, including samples of biological tissue or fluid origin obtainedin vivo or in vitro and biological materials that may be located insitu. Such samples can be, but are not limited to, body fluid (e.g.,blood, blood plasma, serum, or urine), organs, tissues, fractions, andcells isolated from, or located in, mammals including, humans.Biological samples also may include sections of the biological sampleincluding tissues (e.g., sectional portions of an organ or tissue).Biological samples may also include extracts from a biological sample,for example, an antigen from a biological fluid (e.g., blood or urine).Further, the biological sample may include two or more samples that forma tissue micro array.

A biological material may include any material regardless of itsphysical condition, such as, but not limited to, being frozen or stainedor otherwise treated. In some embodiments, a biological material mayinclude a tissue sample, a whole cell, a cell constituent, a cytospin,or a cell smear. In other embodiments, a biological material may be anin situ tissue target, if successive images of the targeted tissue canbe obtained, first with the reference dye and subsequently with theadditional dyes. A tissue sample may include a collection of similarcells obtained from a tissue of a biological subject that may have asimilar function. In some embodiments, a tissue sample may include acollection of similar cells obtained from a tissue of a human. Suitableexamples of human tissues include, but are not limited to, (1)epithelium; (2) the connective tissues, including blood vessels, boneand cartilage; (3) muscle tissue; and (4) nerve tissue. The source ofthe tissue sample may be solid tissue obtained from a fresh, frozenand/or preserved organ or tissue sample or biopsy or aspirate; blood orany blood constituents; bodily fluids such as cerebral spinal fluid,amniotic fluid, peritoneal fluid, or interstitial fluid; or cells fromany time in gestation or development of the subject. In someembodiments, the tissue sample may include primary or cultured cells orcell lines.

In some embodiments, a biological sample includes tissue sections fromhealthy or diseased tissue samples (e.g., tissue sections from colon,breast tissue, prostate). A tissue section may include a single part orpiece of a tissue sample, for example, a thin slice of tissue or cellscut from a tissue sample. In some embodiments, the same section oftissue sample may be analyzed at both morphological and molecularlevels.

As used herein, the term “fluorescent imaging agent” refers tofluorophores that are chemical compounds, which when excited by exposureto a particular wavelength of light, emit light at a differentwavelength. Fluorophores may be described in terms of their emissionprofile, or “color.” Green fluorophores (for example Cy3, FITC, andOregon Green) may be characterized by their emission at wavelengthsgenerally in the range of 515-540 nanometers. Red fluorophores (forexample Texas Red, Cy5, and tetramethylrhodamine) may be characterizedby their emission at wavelengths generally in the range of 590-690nanometers. Examples of fluorophores include, but are not limited to,4-acetamido-4′-isothiocyanatostilbene-2,2′disulfonic acid, acridine,derivatives of acridine and acridine isothiocyanate,5-(2′-aminoethyl)aminonaphthalene-1-sulfonic acid (EDANS),4-amino-N-[3-vinylsulfonyl)phenyl]naphthalimide-3,5 disulfonate (LuciferYellow VS), N-(4-anilino-1-naphthyl)maleimide, anthranilamide, BrilliantYellow, coumarin, coumarin derivatives, 7-amino-4-methylcoumarin (AMC,Coumarin 120), 7-amino-trifluoromethylcouluarin (Coumaran 151),cyanosine; 4′,6-diaminidino-2-phenylindole (DAPI),5′,5″-dibromopyrogallol-sulfonephthalein (Bromopyrogallol Red),7-diethylamino-3-(4′-isothiocyanatophenyl)-4-methylcoumarin,4,4′-diisothiocyanatodihydro-stilbene-2,2′-disulfonic acid,4,4′-diisothiocyanatostilbene-2,2′-disulfonic acid,5-[dimethylamino]naphthalene-1-sulfonyl chloride (DNS, dansyl chloride),eosin, derivatives of eosin such as eosin isothiocyanate, erythrosine,derivatives of erythrosine such as erythrosine B and erythrosinisothiocyanate; ethidium; fluorescein and derivatives such as5-carboxyfluorescein (FAM), 5-(4,6-dichlorotriazin-2-yl)aminofluorescein (DTAF),2′7′-dimethoxy-4′5′-dichloro-6-carboxyfluorescein (JOE), fluorescein,fluorescein isothiocyanate (FITC), QFITC (XRITC); fluorescaminederivative (fluorescent upon reaction with amines); IR144; IR1446;Malachite Green isothiocyanate; 4-methylumbelliferone; orthocresolphthalein; nitrotyrosine; pararosaniline; Phenol Red,B-phycoerythrin; o-phthaldialdehyde derivative (fluorescent uponreaction with amines); pyrene and derivatives such as pyrene, pyrenebutyrate and succinimidyl 1-pyrene butyrate; Reactive Red 4 (Cibacron®Brilliant Red 3B-A), rhodamine and derivatives such as6-carboxy-X-rhodamine (ROX), 6-carboxyrhodamine (R6G), lissaminerhodamine B sulfonyl chloride, rhodamine (Rhod), rhodamine B, rhodamine123, rhodamine X isothiocyanate, sulforhodamine B, sulforhodamine 101and sulfonyl chloride derivative of sulforhodamine 101 (Texas Red);N,N,N′,N′-tetramethyl-6-carboxyrhodamine (TAMRA); tetramethyl Rhodamine,tetramethyl rhodamine isothiocyanate (TRITC); riboflavin; rosolic acidand lathanide chelate derivatives, quantum dots, cyanines, pyreliumdyes, and squaraines.

For applications that additionally use probes, as used herein, the term“probe” refers to an agent having a binder and a label, such as a signalgenerator. In some embodiments, the binder and the label are embodied ina single entity. The binder and the label may be attached directly(e.g., via a fluorescent molecule incorporated into the binder) orindirectly (e.g., through a linker, which may include a cleavage site)and applied to the biological sample in a single step. In alternativeembodiments, the binder and the label are embodied in discrete entities(e.g., a primary antibody capable of binding a target and an enzyme or asignal generator-labeled secondary antibody capable of binding theprimary antibody). When the binder and the label are separate entitiesthey may be applied to a biological sample in a single step or multiplesteps. As used herein, the term “fluorescent probe” refers to an agenthaving a binder coupled to a fluorescent signal generator. These methodsand systems are not limited to any specific imaging agents,morphological dyes, biomarkers or probes. Any fluorescent ornon-fluorescent dye or imaging agent that enables some informativeaspect or feature of a biological material to be actually orartificially visualized so that it can be digitally imaged andprocessed, would be suitable. Suitable dyes and imaging agents include,but are not necessarily limited to, cytological or morphological dyes,immunological dyes such as immunohisto- and immunocyto-chemistry dyes,cytogenetical dyes, in situ hybridization dyes, cytochemical dyes, DNAand chromosome markers, and substrate binding assay dyes.

The methods and systems may be adapted for, but are not limited to, usein analytical, diagnostic, or prognostic applications such as analytedetection, histochemistry, immunohistochemistry, or immunofluorescence.In some embodiments, the methods and systems may be particularlyapplicable in histochemistry, immunostaining, immunohistochemistry,immunoassays, or immunofluorescence applications. In some embodiments,the methods and systems may be particularly applicable in immunoblottingtechniques, for example, western blots or immunoassays such asenzyme-linked immunosorbent assays (ELISA).

FIGS. 2A and 2B illustrate techniques that may be employed to acquireimages for use in certain embodiments. FIG. 2A is a schematic diagram ofa two-step method of image acquisition suitable for use with the presenttechniques. In the first step, only one fluorescent dye, e.g., DAPI isused to stain the tissue. A pre-determined set of four filter cubes maybe used sequentially to obtain images of the DAPI emission wavelength aswell as wavelengths associated with CFP, Cy3 and Cy5 tissueautofluorescence emission wavelengths. In the second step, the tissuesample is removed from the microscope and immunostained with additionalfluorescent dyes that are associated with probes or other moleculesspecific for a marker of interest. The procedure mentioned above is thenrepeated on this stained tissue sample to acquire another set of imagesusing the same four wavelengths. These images contain an unknowncombination of autofluorescence, Cy3 and Cy5 dye signals from the fourchannels. In one embodiment, the images acquired from the first step areregistered with images obtained from the second step, using the DAPIchannel as a registration guide. Following registration using the DAPIchannel, the present techniques may be used to estimate theautofluorescence of the images. An advantage of the two-step method isthat the autofluorescence estimate is obtained at the same part of thespectrum as the fluorescence due to dye. In addition to providinginformation about nuclear location in the images, DAPI images acquiredin both steps are used to register the two image sets. However the DAPIimages contain only local image features. An additional autofluorescenceimage at wavelengths between the DAPI and Cy3 response channels isobtained, using a filter cube matched to the spectral response of CyanFluorescent Protein (CFP). Note that since the tissue sample is notstained with CFP, this image captures only the autofluorescence signaland is characterized by global image features. Thus, to combine bothglobal and local feature information for image registration purposes,the DAPI and CFP images can be added to form composite images.

In general, given a pair of observed tissue images X1_(obvs) andX2_(obvs) with different dye signal to autofluorescence ratios, theimages are related to the underlying true (autofluorescence-free) dyeand the separated autofluorescence images as follows;

$\begin{matrix}{\left. \left. \begin{matrix}{{X\; 1_{obvs}} = {{a_{11}X_{dye}} + {a_{12}X_{af}}}} \\{{X\; 2_{obvs}} = {{a_{21}X_{dye}} + {a_{22}X_{af}}}}\end{matrix} \right\}\Rightarrow\begin{bmatrix}{X\; 1_{obvs}} \\{X\; 2_{obvs}}\end{bmatrix} \right. = {\begin{bmatrix}a_{11} & a_{12} \\a_{21} & a_{22}\end{bmatrix}\begin{bmatrix}X_{dye} \\X_{af}\end{bmatrix}}} & (1)\end{matrix}$In the two-step experiment, there are two image observations for eachdye channel, with one image being purely autofluorescence in thatchannel. Thus, denoting the pair of images from each channel byX1_(obvs) and X2_(obvs) the above equation becomes;

$\begin{matrix}{\begin{bmatrix}{X\; 1_{obvs}} \\{X\; 2_{obvs}}\end{bmatrix} = {\begin{bmatrix}0 & a_{12} \\a_{21} & a_{22}\end{bmatrix}\begin{bmatrix}X_{dye} \\X_{af}\end{bmatrix}}} & (2)\end{matrix}$

In cases where the number of tissue samples to be analyzed is large, itmay not be practical to use the two-step procedure for imageacquisition. Furthermore, a single step process may provide theadvantage of reduced artifacts being introduced in the images due toimage registration as well as damage to the tissue during removal of thecoverslip before immunostaining. Accordingly, in certain embodiments itmay be advantageous to acquire images using an “extra-channel” method, aschematic diagram of which is shown in FIG. 2B. The extra-channel methodis a single step method that acquires images of the stained tissue, withvarying dye signal to autofluorescence ratios, in more channels thanthere are dyes.

In the extra-channel method, the tissue sample is stained with DAPI andimmunostained with antibodies conjugated to Cy3 and Cy5. Other than thethree filter cubes matched to the emission spectra of the three dyes,the extra-channel method may use three extra cubes matched to CFP andfar-red light at both 595 nm (RED1) and 624 nm (RED2). In oneembodiment, the CFP channel measures the autofluorescence signalsimilarly to that from the Cy3 channel, and, for example, the filters at595 nm and 695 nm record an unknown mixture of the excitations fromtissue autofluorescence and dyes in the Cy3 and Cy5 channels.

The autofluorescence spectrum is generally wide-band anddye-independent. Hence, images of the autofluorescence signal atwavelengths close to, but not coinciding with, those of the Cy3 and Cy5dye emission spectra can be used to estimate and subsequently remove thespectrum of the autofluorescence signal in the dye channels according tothe present techniques.

The present techniques may be used to model the additional observationsfrom the extra-channel method. These observations are a combination ofvarying ratios of Cy3 signal to the autofluorescence at the Cy3 emissionwavelength and Cy5 dye signal to Cy5 channel autofluorescence. Theobserved images may be modeled as unknown linear combinations of thetissue autofluorescence and autofluorescence-free dye images in the fiveobservation channels, namely Cy3, Cy5, CFP, RED1 and RED2. The imagesfrom Cy3 and CFP are primarily Cy3 dye and Cy3 autofluorescence signals,respectivelyCY3_(obvs) =a ₁₁ ×CY3_(dye) +a ₁₂ ×CY3_(af)CFP _(obvs) =a ₂₂ ×CY3_(af)  (3a)

Similarly the observed images from the Cy5 and RED channels are relatedto the true dye and autofluorescence signals as;RED1_(obvs) =a ₃₁ ×CY3_(dye) +a ₃₂ ×CY3_(af) +a ₃₃ ×CY5_(dye) +a ₃₄×CY5_(af)RED2_(obvs) =a ₄₂ ×CY5_(dye) +a ₄₃ ×CY3_(af) +a ₄₄ ×CY5_(af)CY5_(obvs) =a ₅₃ ×CY5_(dye) +a ₅₄ ×CY5_(af)  (3b)Equations (3a) and (3b) are valid for all pixels that do not belong tothe background of any observed image appearing in that equation. Inmatrix form, equations (3a) and (3b) can be written as:

$\begin{matrix}{\begin{bmatrix}{{CY}\; 3_{obvs}} \\{CFP}_{obvs} \\{{RED}\; 1_{obvs}} \\{{RED}\; 2_{obvs}} \\{{CY}\; 5_{obvs}}\end{bmatrix} = {\begin{bmatrix}a_{11} & a_{12} & 0 & 0 \\0 & a_{22} & 0 & 0 \\a_{31} & a_{32} & a_{33} & a_{34} \\0 & a_{42} & a_{43} & a_{44} \\0 & 0 & a_{53} & a_{54}\end{bmatrix}\begin{bmatrix}{{CY}\; 3_{dye}} \\{{CY}\; 3_{af}} \\{{CY}\; 5_{dye}} \\{{CY}\; 5_{af}}\end{bmatrix}}} & (4)\end{matrix}$

The present techniques also account for sizeable interactions betweenthe Cy3 and Cy5 channels. For instance, the model allows possiblysignificant cross talk between Cy3 and Cy5 images, even though thetheoretical responses of these channels indicate that there is minimaloverlap between the spectra of the two channels. This is done inanticipation of the observed red-shift of emission spectra in tissuesamples. Since no prior knowledge of the proportions in which thedifferent true images contribute to the observations is assumed, boththe matrix of mixing coefficients and the vector of true image pixels onthe right hand side of equation (4) are unknown. Physical observationsindicate that the true dye and autofluorescence images may be assumed tobe statistically independent making the system of equations solvable.

Expression of a specific protein or structure in the autofluorescenceimage of a tissue sample is no indication of its presence or absence inan image of the sample after a protein-specific dye has been used tostain it. Random observations may be statistically independent if thepresence of one gives no information about the other. Mathematically,random vectors x and y may be statistically independent if and only iftheir joint probability density can be factorized into a product oftheir marginal probability densities;P(x,y)=P _(X)(x)×P _(Y)(y)  (5)It follows that the true autofluorescence image of a tissue spot isstatistically independent of its true (autofluorescence-free) dye image.This is true for many applications. Exceptions are situations in whichthe biomarker binds to a tissue structure (e.g. lipid droplet) that hassignificant intrinsic autofluorescence, distinct from other tissuecomponents.

Since the dyes are targeted to detect specific proteins and the AFsignals have tissue-dependent pixel intensities, these images can beassumed to be observations drawn from non-Gaussian, often bimodal,distributions.

Regardless of the manner in which the images are acquired, the presenttechniques may be applied to the acquired images in order to reduceand/or remove any inherent autofluorescence in the images. In oneembodiment, the present techniques provide a Joint Estimation Techniquethat includes Non-negative Matrix Factorization. Non-negative MatrixFactorization (NMF) is a technique of decomposing a matrix ofnon-negative observations into a product of two matrices, each of whichhas only non-negative elements. NMF may use the Euclidean squareddistance cost function and the corresponding multiplicative update rule.

The present techniques allow observed images to be described as unknownlinear combinations of an underlying signal image (due to fluorescenceof interest) and an autofluorescence image, plus an unknown offset, dueto dark current. The term m may be defined to be the number of suchimages acquired and the term n to be the number of pixels in each imagewhile the term e_(i) may be defined to be the camera exposure time forthe i^(th) image, where i is any integer such that 0≦i≦m. The valuese_(i) may be recorded when the images are acquired and, thus, may be aknown parameter input to the present techniques. In specificembodiments, charge-coupled device cameras attached to fluorescentmicroscopes, like many other radiation receptors, exhibit a constantresponse even in the absence of light. This offset, known as “darkcurrent” may vary, for example due to changes in temperature. Thenon-negative real number d_(i) may be defined to be the dark current forthe i^(th) image, where i is an integer such that 0≦i≦m. The variabled_(i) is constrained to be non-negative since dark current effects arealways additive. The values d_(i) are unknown parameters of the presentmodel. The real 1×n row vector is defined as I_(OBS) ^(i), whose entriesare the pixels of the i^(th) acquired image, where i, is an integer suchthat 0≦i≦m. The i^(th) entry of the real 1×n row vector I_(AF), isdefined to be the intensity of autofluorescence due to tissue at pixellocation j, for each integer j such that 1≦j≦n. The j^(th) entry of thereal 1×n row vector I_(SIG) is defined to be the intensity offluorescence of interest at pixel location j, for each integer j suchthat 1≦j≦n. In one embodiment, I_(OBS) ^(i) is a linear combination ofI_(AF) and I_(SIG) with coefficients given by the equationI _(OBS′) ^(i) =e _(i)((b _(i′1) ×I _(SIG))+(b _(i′2) ×I _(AF))+d_(i)),  (6)where b_(i,1) and b_(i,2) are non-negative real numbers, for everyinteger i such that 1≦i≦m. Equation (6) is a spectral mixing model, andrepresents the physical situation giving rise to the observed images.More specifically, the observed images I_(OBS) ^(i) are written aslinear combinations of two underlying images: I_(SIG) (denoting thefluorescence of interest), and I_(AF) (denoting the autofluorescence).The unknown dark current terms d_(i) and the known exposure times e_(i)act as a shift and a scale factor (respectively).

The algorithm of the present techniques may estimate b_(i,1), b_(i,2),I_(AF), and I_(SIG) given I_(OBS) ^(i) for each integer i such that0≦i≦m. In other words, the algorithm calculates an image (denotedI_(AF)) that represents autofluorescence and an image (denoted I_(SIG))which represents fluorescence of interest. In addition, the algorithmcalculates coefficients b_(i,j) which specify how the images I_(AF) andI_(SIG) are combined to form the observed images (denoted I_(OBS) ^(i)),each of which may contain some autofluorescence and some fluorescence ofinterest.

In certain embodiments of the present technique, a matrix A may bedefined as the real m×n matrix A according to the formula

$\begin{matrix}{{A = \begin{bmatrix}\underset{\_}{I_{OBS}^{1}} \\\vdots \\\overset{\_}{I_{OBS}^{m}}\end{bmatrix}},} & (7)\end{matrix}$where I_(OBS) ^(i) is defined in equations (3a) and (3b), for eachinteger i such that 1≦i≦m. The images in the rows of A are the inputs tothe algorithm and contain unknown mixtures of autofluorescence andfluorescence of interest plus an unknown dark current term times a knownexposure time. The matrix A is defined as the observation matrix. Theentries of A are non-negative since they represent image pixels.

In certain embodiments of the present technique, a matrix C may bedefined as the real 2×n matrix C according to the formula

$\begin{matrix}{{C = \left\lbrack \frac{I_{SIG}}{I_{\Delta\; F}} \right\rbrack},} & (8)\end{matrix}$The first row of C contains an estimate of the component due tofluorescence of interest, in the images in the matrix A. The second rowof C contains an estimate of the component due to autofluorescence, inthe images in the matrix A. The matrix C is known as the source matrix.The entries in C are non-negative since they represent image pixels.

In certain embodiments of the present technique, a matrix B may bedefined wherein the (i,j) entry of the real i×2 matrix B may be b_(i,j),where b_(i,j) satisfies equation (6), for any integers i and j such that1≦i≦m and 1≦j≦n. The entries in B specify how much autofluorescence andhow much fluorescence of interest is present in each of the images in A,according to equation (6). More specifically, b_(i,1) and b_(i,2)specify how much fluorescence of interest and autofluorescence(respectively) is in I_(OBS) ^(i), for any integer i such that 1≦i≦m,where I_(OBS) ^(i) is defined in equations (3a) and 3(b). It followsthat the ratio of autofluorescence to fluorescence of interest in theimage in the i^(th) row of A is

$\begin{matrix}{\frac{b_{i,2}}{b_{i,1}},} & (9)\end{matrix}$for any integer i such that 1≦i≦m. The matrix B is known as the mixingmatrix. Since the entries of B are non-negative, equation (6) isphysically interpretable.

In certain embodiments of the present technique, a matrix D may bedefined wherein the (i,j) entry of the real m×n matrix D may be d_(i),defined in equation (6). It follows that all columns of D are identical,and hold the dark currents d_(i), of each of the m images. Since darkcurrent acts additively, the variables d_(i), are constrained to benon-negative, so the entries of D are all non-negative.

In certain embodiments of the present technique, a matrix E may bedefined to be the real, diagonal, m×m matrix with the exposure times ofthe observed images I_(OBS′) ^(i) as diagonal entries. In other words,the i^(th) diagonal entry of E is defined to be where the term e_(i), isdefined in equation (1), and i is any integer such that 0≦i≦M. Sincee_(i) represents time, all the entries in E are non-negative.

It follows from equation (6), and the definitions of A, B, C, D, and E,respectively, thatA=E(BC+D).  (11)All the entries in all the matrices in equation (11) are non-negative.Therefore, the model of the present techniques constitutes anon-negative matrix factorization model for autofluorescence ofbiological tissue, acquired by an imaging device with a variable darkcurrent term, such as a charge-coupled device camera attached to afluorescent microscope. Because the exposure times in the matrix E andthe dark current terms in the matrix D are part of the model, equation(11) is a normalized non-negative matrix factorization.

One disadvantage of previous non-negative matrix factorizationalgorithms has been convergence to local minima. The present algorithmincludes a novel step designed to reduce these occurrences using aGaussian kernel to smooth the images at every iteration. In certainembodiments, the smoothing factor is reduced at later iterations, andthe final iterations may continue without any smoothing. Regularizationof the computed solution incorporates the prior knowledge that changesin the image on a scale smaller than the standard deviation of thekernel are irrelevant. This helps to constrain the solution computed bythe algorithm, reducing the probability of undesirable local minima.

An alternating constrained least squares approach may be used to solveequation (11). The matrices B and C may be initialized in anapplication-specific way. Then, the following three steps may berepeated until convergence. The first step is to estimate B and D,holding C fixed. The second step is to estimate C, holding B, and Dfixed. The third step is to smooth the images in the rows of C, using aGaussian kernel, whose standard deviation decreases with each iteration.The initialization of B, C, and D depends on the specific circumstancesunder which the algorithm is used.

The first step of the present algorithm is to estimate B and D, holdingC fixed. More specifically, the new matrices B and D solve theoptimization problem

$\begin{matrix}{\left\lbrack B \middle| D \right\rbrack = {\begin{matrix}{\arg\;\min} \\\left\{ {\overset{\sim}{B},{{\overset{\sim}{D}\mspace{11mu}\text{:}\mspace{11mu}{\overset{\sim}{b}}_{i,j}} \geq 0},{\overset{\sim}{d}}_{i,j}} \right\}\end{matrix}{{{A - {{E\left\lbrack B \middle| D \right\rbrack}\left\lbrack \frac{C}{1} \right\rbrack}}}.}}} & (12)\end{matrix}$That is, the matrices B and D minimize the reconstruction error∥A−E[B|D][C/1]∥subject to the constraint that all entries in B and D must benon-negative. Equation (12) is an instance of a non-negativelyconstrained least squares problem. A solution to a non-negativelyconstrained least squares problem is a vector that satisfies a set oflinear equations with minimal error, subject to having only non-negativeentries. Suppose p, and q are positive integers. Suppose M is a real p×qmatrix, and y is a real p×1 column vector. The non-negativelyconstrained least squares problem is to find a real q×1 column vector,x, such that∥mx−y∥  (12.1)is as small as possible, subject to the constraint that for each integeri, such that 1≦i≦q, (12.2) and x_(i)≧0. The algorithm minimizes (12.1)subject to (12.2). Suppose that w, and z are real q×1 column vectors.Suppose that Mp is a real p×q matrix. Suppose that P, and Z are sets ofintegers. The set P contains the indices of the non-zero (active)variables in the current solution x, and Z contains the indices of thezero (inactive) variables, in the current solution, x. The vector w isthe dual vector of x.

The second step of the present algorithm is to estimate C, holding B andD fixed. More specifically, the new matrix C solves the optimizationproblem

$\begin{matrix}{C = {\begin{matrix}{\arg\;\min} \\\left\{ {{\overset{\sim}{C}\;\text{:}\mspace{11mu}{\overset{\sim}{c}}_{i,j}} \geq 0} \right\}\end{matrix}{{A - {{E\left( {{BC} + D} \right)}.}}}}} & (13)\end{matrix}$That is, the matrix C minimizes the reconstruction error ∥A−E(BC+D)∥subject to the constraint that all entries in C must be non-negative.Equation (13) is an instance of a non-negatively constrained leastsquares problem that may be solved as described herein.

The third step of the present algorithm is to smooth the images I_(SIG)and I_(AF), in the rows of C. Every pixel value is replaced by aweighted average of nearby pixel values. The weights are given by aGaussian kernel

$\begin{matrix}{\frac{1}{\sqrt{2{\pi\sigma}^{2}}}{\mathbb{e}}^{\frac{r^{2}}{{2\sigma^{2}},}}} & (14)\end{matrix}$where r is the distance to the current pixel. The value of the parametera decreases at each iteration. This step of the algorithm is designed toregularize the convergence of the algorithm, thus reducing the risk ofconverging into local minima.

In specific embodiments of the present techniques, as defined inequation (7) A has m rows of length n, each of which contains an imageacquired according to the present techniques. For the purposes of theexamples provided below, the number of images used in each run of thealgorithm was m=4 and the number of pixels in each image was n=1205824.The term J_(OBS) ^(i,j) may be defined to be the image acquired in stepi of the examples provided herein, using filter cube number j, where iand j are positive integers. The specific images in the rows of A either

$\begin{matrix}{A = \left\lbrack \frac{\frac{J_{OBS}^{4,5}}{J_{OBS}^{2,5}}}{\frac{J_{OBS}^{2,1}}{J_{OBS}^{4,1}}} \right\rbrack} & (17) \\{A = \left\lbrack \frac{\frac{J_{OBS}^{4,5}}{J_{OBS}^{2,5}}}{\frac{J_{OBS}^{2,4}}{J_{OBS}^{4,4}}} \right\rbrack} & (18)\end{matrix}$where J_(OBS) Is defined above. Row 1 of A contains an extra channelautofluorescence estimate. Rows 2 and 3 of A contain two stepautofluorescence estimates. Row 4 contains an image intended to captureas much signal as possible with as little autofluorescence as possible.When A is defined by equation (17) (respectively, equation (18)), theimage in row 4 is intended to capture as much fluorescence due to cy5(respectively, cy3) as possible, with as little autofluorescence aspossible.

As defined in equations (2) and (3), the matrix D has n identicalcolumns of length m, each of which contains dark current estimates d_(i)for the observed images I_(OBS) ^(i). The dark current estimate d_(i)for I_(OBS) ^(i) is initialized to the 5^(th) percentile of the imagehistogram of I_(OBS) ^(i). That is, d_(i) is the value of a pixel inI_(OBS) ^(i) which is brighter than exactly 5 percent of pixels inI_(OBS) ^(i). These values are updated at each iteration of thenon-negative matrix factorization algorithm.

As defined in equations (4), (5), and (8), the first row of C is I_(SIG)(an estimate for the fluorescence of interest), and the second row of Cis I_(AF) (an estimate for the autofluorescence). The second row of C isinitialized to a weighted average of the rows of A containing either twostep or extra channel autofluorescence estimates, which are normalizedby subtraction of the estimated dark current and division by theexposure time. To be more precise, for each integer i such that 1≦i≦m−1,(row 2 of C)=Σ_(i=1) ^(m−1) ^(wi) ((row i of A)−d _(i))/e _(i),  (19)where the rows of A are as defined in equation (17) or (18), d_(i) hasthe values described in the previous paragraph, and e_(i) is defined inequation (1). The values of the weights w_(i) in equation (19) are

$\begin{matrix}{{w_{1} = \frac{1}{4}},{w_{2} = \frac{1}{4}},{w_{3} = {\frac{1}{2}.}}} & (20)\end{matrix}$The matrix B is initialized by solving the optimization problem

$\begin{matrix}{b = {\begin{matrix}{\arg\;\min} \\\left\{ {{\overset{\sim}{B}\mspace{11mu}\text{:}\mspace{11mu}{\overset{\sim}{b}}_{i,j}} \geq 0} \right\}\end{matrix}{{A - {E\left( {\left\lbrack B \middle| D \right\rbrack\begin{bmatrix}C \\1\end{bmatrix}} \right)}}}}} & (21)\end{matrix}$where the matrices A, C, and D initialized as described in the previoustwo paragraphs, and the matrix E is defined above. Equation (21) is aninstance of a non-negatively constrained least squares problem. Thevalue of the parameter σ, introduced in equation (14) was defined to be2 in the first iteration, 1.8 in the second iteration, 1.6 in the thirditeration 1.4 in the fourth iteration, 1.2 in the third iteration, 1 inthe fifth iteration, and 0 in all subsequent iterations.

With the forgoing in mind, the following examples provide specificembodiments in which the present techniques have been applied. Theconcentration of antigens such as estrogen receptor, PCAD, and HER2 inhuman breast biopsies was analyzed. Fluorescent dyes in the cyaninefamily (cy3 and cy5) were bound to these antigens by using acorresponding antibody. In addition, the dye4′,6-diamidino-2-phenylindole DAPI) was used to stain cell nuclei. Afluorescence microscope and filters as described herein were used toexcite the dyes and measure corresponding emission. The autofluorescenceseparation algorithm described above was used to separate thefluorescence due to dye with that due to tissue.

The experimental protocol used multiplexing, which refers to staining asample with more than one dye at a time, removing that dye, stainingagain, and repeating the process many times over. The samples wereinitially stained with DAPI and then images were taken with each of thefilter cubes listed in Table I. The samples were then stained with Cy3bound to PCAD, and Cy5 bound to estrogen receptor. Images were thentaken with each of the filter cubes listed in Table I. When the sampleswere removed from the stage and then replaced, the location on the stageis inevitably slightly different, so the images taken were thenregistered to compensate for the misalignment. This was accomplishedusing a technique based on mutual information.

In one application of the present techniques, fluorescent beads having adiameter of 1 micron (Polysciences Inc., Warrington, Pa., catalog number18660) were embedded in tissue samples. A fluorescence microscope (axioimager upright model from Carl Zeiss, with a SCAN 130×85 piezodrivestage manufactured by Marzhauser Wetziar) was used to excite the samplesand measure the corresponding emission. Images were acquired of thesample both before and after addition of fluorescent beads. Filters,called “excitation filters”, were used to block light not havingwavelengths in a certain range, thus controlling the wavelengths oflight exciting the sample. Different filters, called “emission filters”,were used to measure the energy of light emitted in certain spectralranges, by blocking light not having wavelengths in that range. Thefilters were arranged in cubes consisting of one excitation filter, oneemission filter, and a dichroic mirror (see Table I). Autofluorescenceseparation algorithms according to the present techniques were used toseparate the fluorescence due to the beads with that due to tissue. Thefilter cubes in Table I are intended to measure the fluorescence of acertain dye or to measure autofluorescence, although spectral overlapbetween dyes' spectra and the autofluorescence spectrum means that eachfilter cube inevitably measures a combination of these. The filter cubesnumbered 1, 2, and 4 in Table I are designed to match the excitation andemission wavelengths of the dyes cy5, cy3, and DAPI (respectively), asclosely as possible. On the other hand, the filter cube numbered 3 inTable I has excitation and emission spectra that have a relatively smalloverlap with those of cy3, cy5, and DAPI. Therefore, filter cube 3measures more autofluorescence than fluorescence due to dye. Under theassumption that autofluorescence is roughly the same at differentwavelengths, filter cube 3 can be used to measure autofluorescence atall wavelengths.

TABLE I FILTER CUBES USED IN THE EXPERIMENTAL PROTOCOL. Filter Cube PartExcitation Emission Dichroic Spectra No. Vendor number filter filtermirror Correspond no. 1 Chroma 41024 HQ620/60x HQ665LP Q660LP cy5 dye 2Zeiss 43HE BP550/25 BP605/70 570 cy3 dye 3 Semrock 2432A- FF01- FF01-FF458- autofluorescence 000- 438/24 438/32 Di01 ZERO 4 Zeiss 49 365BP445/50 395 DAPI dye

The outputs from autofluorescence separation algorithms were compared toground truth images consisting of only fluorescent beads, with noautofluorescence due to tissue. The beads were chosen to fluoresce muchmore brightly than tissue at the excitation and emission wavelengths offilter cube number 2. Therefore an image taken with that filter cube(see, e.g., FIG. 3A) may be thresholded so that only the beads arevisible and tissue autofluorescence is not present. Images taken withfilter cube number 2 are ground truth with which algorithm results arecompared.

The algorithm of the present techniques was applied in the followingway. The algorithm was given four images, I_(OBS) ¹, I_(OBS) ², I_(OBS)³, and I_(OBS) ⁴, defined in equation (3). Of these, I_(OBS) ¹, I_(OBS)², and I_(OBS) ³, were obtained using filter cubes 1, 2, and 3(respectively) before the beads were added to the sample. On the otherhand, I_(OBS) ⁴, (FIG. 3A) was obtained using filter cube 3, afteraddition of beads to the sample. In both steps, before and after thebeads are added, DAPI images are collected to aid the imageregistration. Note that the beads are placed on top of a tissue stainedwith DAPI. The beads were brighter than autofluorescence in the groundtruth image (FIG. 3A), the ratio of the beads' brightness to theautofluorescence's brightness in I_(OBS) ⁴ (FIG. 3B) was comparable tothe signal to noise ratio in images of stained tissue (FIG. 3A). Allfour images were represented in the same coordinate system, byregistering the DAPI images. The registration was based on minimizing amutual information metric between the first and the second image. Theestimation was done in multiple resolutions from coarse to fine. After15 iterations of the algorithm of the present techniques, the imageI_(SIG) defined in equation (5), was obtained (FIG. 3C). The groundtruth image (FIG. 3A) resembles I_(SIG) (FIG. 3C), indicating successfulremoval of autofluorescence was accomplished. Receiver operatorcharacteristic (ROC) analysis was used to quantify that similarity. Morespecifically, a threshold was chosen such that pixels above thatthreshold in the ground truth image (FIG. 3A) belong to a bead, andpixels below that threshold do not. In addition, I_(SIG) (FIG. 3C) wasthresholded at a variable threshold t, that took 100 values between theminimum and maximum pixel values in I_(SIG). For each value of t, thosepixels whose value exceeded t were predicted by the algorithm to bebeads. By comparison with the thresholded ground truth image (FIG. 3A),a false positive rate and a true positive rate were calculated, for eachvalue of t.

The algorithm of the present techniques was compared to other techniquessuch as image subtraction, non-normalized nonnegative matrixfactorization, and principal component analysis by two-sample t-tests.The results were plotted as a receiver operator characteristic (ROC)curve, as shown in FIG. 4. This procedure was repeated 35 times, for 35different tissue samples. The mean of the 35 ROC curves was calculated.The areas under 35 ROC curves (AUC) were calculated for normalizednon-negative matrix factorization (reference 40), image subtraction(reference 42), non-normalized nonnegative matrix factorization(reference 44), and principal component analysis (reference 46). Threet-tests were performed. Each t-test compared the areas under 35 ROCcurves for a previous state of the art method, with the areas under 35ROC curves for the algorithm of the present paper. In each case, theresults were significant, with a p-value less than 0.01, showing thatthe present techniques lead to higher AUCs than previous methods (TableII). The usefulness of the dark current matrix D (Subsection II-D) wasdemonstrated by comparing the normalized, non-negative matrixfactorization to the non-normalized, non-negative matrix factorizationwith no D term in the model. Exactly the same inputs and validationprocedure were used, but the matrix D was omitted from the algorithm.

TABLE II Significance level Method (p-value) Image substraction 7.8E−06Non-normalized 3.6E−11 Non-negative matrix factorization Principalcomponent 2.9E−08 analysis

FIGS. 5A and 5B are examples of an input and an output, respectively,for the present techniques. FIG. 5A is an image of a human breast biopsystained with Cy5 bound to estrogen receptor, as well as autofluorescencedue to tissue. After 15 iterations of the presently disclosed algorithm,the output I_(SIG), defined in equation (5), was obtained (FIG. 5B).This image is an estimate for the fluorescence due to Cy5, without theautofluorescence due to tissue.

While only certain features of the invention have been illustrated anddescribed herein, many modifications and changes will occur to thoseskilled in the art. It is, therefore, to be understood that the appendedclaims are intended to cover all such modifications and changes as fallwithin the true spirit of the invention.

The invention claimed is:
 1. A method for reducing autofluorescence inan image of a biological material, comprising the steps of: accessingimage data from two or more images of the biological material, whereinat least one of the images is fluorescently stained for a marker ofinterest and wherein at least one of the images is a reference image;analyzing the image data of the two or more images using a non-negativematrix factorization algorithm to generate an estimate of theautofluorescence in at least one of the two or more images; andgenerating an output of a corrected image with reduced autofluorescence.2. The method of claim 1, comprising iteratively improving the estimateof the autofluorescence.
 3. The method of claim 2, wherein iterativelyimproving the estimate of the autofluorescence comprises smoothing witha Gaussian kernel.
 4. The method of claim 1, wherein the non-negativematrix factorization algorithm comprises an estimate for thecontribution of dark current.
 5. The method of claim 1, wherein thenon-negative matrix factorization algorithm uses as an input the cameraexposure time for each of the two or more images.
 6. The method of claim1, wherein analyzing the image data comprises employing an alternatingconstrained least squares approach.
 7. The method of claim 1, comprisingacquiring the two or more images by a two-step image acquisition or anextra channel image acquisition.
 8. A non-transitory computer-readablemedium comprising instructions for: accessing image data from two ormore images of the biological material, wherein at least one of theimages is fluorescently stained for a marker of interest and wherein atleast one of the images is a reference image; analyzing the image dataof the two or more images using a non-negative matrix factorizationalgorithm to generate an estimate of the autofluorescence in at leastone of the two or more images; and generating an output of a correctedimage with reduced autofluorescence.
 9. The non-transitorycomputer-readable medium of claim 8, comprising instructions foriteratively improving the estimate of the autofluorescence.
 10. Thenon-transitory computer-readable medium of claim 9, wherein theinstructions for iteratively improving the estimate of theautofluorescence comprise smoothing with a Gaussian kernel.
 11. Thenon-transitory computer-readable medium of claim 8, wherein thenon-negative matrix factorization algorithm comprises an estimate forthe contribution of dark current.
 12. The non-transitorycomputer-readable medium of claim 8, wherein the non-negative matrixfactorization algorithm uses as an input the camera exposure time foreach of the two or more images.
 13. The non-transitory computer-readablemedium of claim 8, wherein the instructions for analyzing the image datacomprise employing an alternating constrained least squares approach.14. The non-transitory computer-readable medium of claim 8, comprisinginstructions for acquiring the two or more images by a two-step imageacquisition, or an extra channel image acquisition.
 15. An imageanalysis system comprising: a processor adapted to receive image datafrom two or more images of the biological material, wherein at least oneof the images is fluorescently stained for a marker of interest andwherein at least one of the images is a reference image the processoradapted to run instructions for: analyzing the image data of the two ormore images using a non-negative matrix factorization algorithm togenerate an estimate of the autofluorescence in at least one of the twoor more images; and generating an output of a corrected image withreduced autofluorescence.
 16. The system of claim 15, comprisinginstructions for iteratively improving the estimate of theautofluorescence.
 17. The system of claim 16, wherein the instructionsfor iteratively improving the estimate of the autofluorescence comprisesmoothing with a Gaussian kernel.
 18. The system of claim 15, whereinthe non-negative matrix factorization algorithm comprises an estimatefor the contribution of dark current.
 19. The system of claim 15,wherein the non-negative matrix factorization algorithm uses as an inputthe camera exposure time for each of the two or more images.
 20. Thesystem of claim 15, wherein the instructions for analyzing the imagedata comprise employing an alternating constrained least squaresapproach.
 21. The system of claim 15, comprising instructions foracquiring the two or more images by a two-step image acquisition or anextra channel image acquisition.